Faces get distorted when scaled or moved
It's difficult to see from your screenshot but:

1.) A plane, by definition, is two dimensional.  A face in Blender is simply a plane.  Once you edit the face in a way that destroys the two-dimensionality, Blender doesn't quite know what to do with it, because it expects that the user understand graphics and geometry.

2.) Yes, most certainly.

3.) You must subdivide the face in a way that "allows" it to remain two-dimensional.  Triangular faces, by definition, are two dimensional, because for any three given vertices, they exist in the same plane.  Therefore, subdividing it into triangular faces is the easiest way to resolve this:


4.) Most certainly not.